I always collect the maximum number of pets (usually 3) from rare mobs. Sometimes there are different breeds or I need more than one of them for specific fights...
I would love an option for HandyNotes to only count the reward as completed when I got the maximum number of the specific pet.

I'm going to close this as a bit of a niche request. While there are some cases where having multiples of a pet can make a certain trainer encounter easier, in all of those cases the trainers can also be defeated using a team of unique pets.

In these cases I usually recommend an addon aimed at more hardcore collectors, like All The Things (I'm not sure if it has this option of not).